Why the dat files? The dat files are only used in one way ?
The only element that I don't manage is the DMZ and the firewalls...
All is good from exchange server to the mobile and never good in the other direction...
For the BESADMIN rights I followed scrupulously the installation guide.

Dat files are send for all emails and for sync of device. If the firewall is sent to block the .dat file then the sync will have a problem. We had this problem when we switch from using redirector to BES. We had to make sure our firewall was not blocking the dat files.

BESADMIN was to have rights to each users mail accounts. I know BESADMIN needs Send As rights but I am not sure of the other ones.

In your post with the CDO versions, it looks like you had older CDO on the BES. Make sure they are the same or the BES is higher.

I would doublecheck the permission requirements. Especially the send as/receive as permissions. Domain Admins have send as/receive as denied, so make sure the BESAdmin acct is not in the Domain Admins (but is in local admins).

CDO.dll are now identical to those of exchange 2003 SP1 and the rights are correct

The BesAdmin is local Admin of the BES server and have send as/receive as and manage store: BesAdmin is not domain admin or others...just domain user
(For the BESADMIN rights I followed scrupulously the installation guide.)

An invitation leaves the device with small v green and then a few seconds later red cross (a not indexed message of error)

We have had this issue in the past for single users on our bes not affecting all users. Our solution was to call our provider (Cingular) and have them de-register the blackberry on their network and re-register it. Then go through the enterprise activation again. This has fixed about 6 different 'goofy' issues we have encountered over the past 3 years. Go figure......

When we were on BES 4.0 we had the same issue and it ended up being the secretary deleting the appointment for their boss and the appointment would remain on the bosses calendar because the deleted item goes in to the secretary's deleted items and not the boses deleted items. If the BES did not see the item in the boses deleted items, then it was never moved from his or her calendar. Very difficult ot explain this to users. Fortunately, this was fixed in 4.1.